Univariate Probability Distributions for IIT JAM Statistics

Succeeding in mathematical statistics exams requires a deep, intuitive understanding of how probability distributions behave and how to apply them to solve complex theoretical problems. This comprehensive text-based course walks you through the core concepts of standard univariate distributions. You will transition from basic probability definitions to confidently calculating moments, generating functions, and transforming variables, establishing a rock-solid foundation for competitive exams. What you'll learn: 1. Understand the fundamental properties of discrete and continuous univariate distributions. 2. Calculate expectation, variance, moments, and moment generating functions with precision. 3. Master standard discrete distributions including Binomial, Poisson, and Geometric models. 4. Analyze standard continuous distributions such as Normal, Exponential, Beta, and Gamma. 5. Apply transformation techniques to determine the distribution of functions of random variables. 6. Practice solving exam-style theoretical problems through structured, step-by-step written derivations. The course starts with foundational probability concepts and core terminology before moving into detailed breakdowns of specific discrete and continuous distributions. You will progress through clear mathematical proofs, written explanations, and practical problem-solving strategies designed for self-paced study. This course is designed for university students, IIT JAM aspirants, and anyone seeking a rigorous introduction to mathematical statistics. No advanced background in probability is required, though a basic understanding of calculus is recommended. Start reading today to master univariate distributions and elevate your exam preparation.